Adiabatic Quantum Computing (AQC) is a computational model that utilizes the fascinating aspects of quantum mechanics principles to solve complex problems. It can potentially provide breakthrough speedups for certain computational problems. It's based on the adiabatic theorem in quantum physics which states that if a quantum system remains in its ground state and a Hamiltonian function changes slowly enough, the system will remain in the ground state corresponding to the new Hamiltonian.
The basis of AQC relies on the ability to encode a given computational problem into a suitable Hamiltonian. This Hamiltonian is then slowly evolved from an initial simple form, where the quantum system can be prepared at the ground state, to a final form where the ground state is the solution to the computational problem.
To illustrate this, imagine that we have a computational problem with its solutions described by the Hamiltonian H_problem. The energy of H_problem will correspond to the cost function of the problem, and the lowest energy state, the ground state, will give us the solution.
import numpy as np import scipy.linalg as la # Hamiltonian of the problem H_problem = np.array([[1.0, 0, 0, 0], [0, 4.0, 0, 0], [0, 0, 9.0, 0], [0, 0, 0, 16.0]]) # Ground State, Solution of the problem _, ground_state = la.eig(H_problem) print("Ground State of the problem Hamiltonian : ", ground_state[0])
An initial Hamiltonian H_initial is selected such that its ground state is easy to prepare. In practically implemented AQC systems, H_initial is often a simple quantum system like a uniform magnetic field applied to a bunch of qubits. As the system evolves from H_initial to H_problem, the qubit stays in the ground state if the evolution is done slowly and adiabatically (hence the name).
# Initial Hamiltonian H_initial = np.array([[1.0, 0, 0, 0], [0, 1.0, 0, 0], [0, 0, 1.0, 0], [0, 0, 0, 1.0]]) # Ground State, Easy to prepare _, initial_state = la.eig(H_initial) print("Ground State of the initial Hamiltonian : ", initial_state[0])
Though adiabatic quantum computation and quantum annealing seem alike, a significant difference lies in the error mitigation. In AQC, if the system is always in the ground state of the Hamiltonian, quantum errors can be intrinsically protected. Whereas in quantum annealing, which is a form of heuristic designed for optimization problems, it is more susceptible to quantum errors.
In conclusion, adiabatic quantum computation has tremendous potential offering quantum speedup for certain tasks. The evolution of the field, with the promise of more robust and error-tolerant quantum computation, is certainly an exciting prospect.
Keep in mind, however, that every technology has its challenges. Unwanted interactions and system fragility are the current challenges that the field of AQC needs to overcome. Nonetheless, the active developments in this field make it a fascinating area to watch for the future.